Comparison of NiFeCr and NiFe in ferromagnetic Josephson junctions

Joshua Willard; Nicholas J. Emtage; Norman O. Birge; Reza Loloee; Robert M. Klaes; Swapna Sindhu Mishra

REVIEW 4 major objections 4 minor 65 references

Comparison of NiFeCr and NiFe in ferromagnetic Josephson junctions

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Adding 9% chromium to Permalloy suppresses the Josephson critical current by nearly two orders of magnitude in the π state, making NiFeCr unsuitable as the soft magnetic layer in cryogenic memory junctions.

desk verdict First transport data on NiFeCr Josephson junctions deliver a robust negative result for cryogenic memory; the abstract overstates precision, but the paper is honest and deserves peer review. read the letter →

arxiv 2501.06845 v3 pith:LDFD5757 submitted 2025-01-12 cond-mat.supr-con cond-mat.mes-hallcond-mat.mtrl-sci

Joshua Willard , Swapna Sindhu Mishra , Robert M. Klaes , Nicholas J. Emtage , Reza Loloee , Norman O. Birge This is my paper · ORCID

classification cond-mat.supr-concond-mat.mes-hallcond-mat.mtrl-sci PACS 74.50.+r85.25.Cp

keywords Josephsonjunctionsπ-junctionsferromagneticNiFeCrPermalloycryogenicmemorycriticalcurrent0-πtransition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tests whether Cr-doped Permalloy (Ni73Fe18Cr9) can replace standard Permalloy (Ni80Fe20) as the soft magnetic layer in ferromagnetic Josephson junctions for cryogenic memory. It finds that the alloy lowers the saturation magnetization to about 62% of Permalloy's value, as intended, but at the cost of a supercurrent that is nearly two orders of magnitude smaller in the π state and a decay length of only 0.36 nm, less than half that of NiFe. The 0–π transition moves from 1.49 nm in NiFe to 2.30 nm in NiFeCr, so the ferromagnet thickness needed for a π junction grows almost in proportion to the magnetization drop, leaving the switching energy essentially unchanged. The authors conclude that NiFeCr does not meet the requirements for memory applications that demand π-junctions with large critical current density.

What carries the argument

The analysis is carried by an exponentially damped sinusoidal fit to the critical-current–resistance product, $I_c R_N = V_0 \exp(-d_F/\xi_{F1}) |\sin((d_F - d_{0\pi})/\xi_{F2})|$, where $d_F$ is the ferromagnet thickness. The function is an approximate interpolation between the diffusive-limit and intermediate-limit theories of supercurrent through a ferromagnetic layer, and the fit extracts the decay length $\xi_{F1}$, the oscillation length $\xi_{F2}$, and the first 0–$\pi$ transition thickness $d_{0\pi}$. Those three numbers carry the paper's quantitative claim that NiFeCr suppresses the supercurrent too strongly for memory applications.

What would settle it

Measure the critical current–resistance product for NiFeCr junctions with ferromagnet thickness from 3.7 nm up to roughly 6 nm: Eq. (4) predicts a continued exponential decay and a second 0–$\pi$ transition whose position is fixed by $\xi_{F2} = 0.67$ nm. If the second lobe appears at a thickness incompatible with that prediction, or the decay is not exponential, the reported transition thickness and decay length are model-dependent rather than intrinsic material properties.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a negative result for a proposed material substitution: adding 9% Cr to Permalloy suppresses the Josephson critical current by nearly two orders of magnitude in the π state, and the NiFeCr thickness required to reach the π state increases almost inversely with the decrease in magnetization, so the switching energy is hardly changed. The quantitative signatures are the fitted values of the critical-current–resistance product versus ferromagnet thickness: a 0–π transition at $d_{0\pi} = 2.30 \pm 0.01$ nm, a decay length $\xi_{F1} = 0.36 \pm 0.01$ nm, and an oscillation length $\xi_{F2} = 0.67 \pm 0.03$ nm, compared with 1.49 nm, 0.67 nm, and 0.85 nm for NiFe. The paper reads these numbers as evidence that NiFeCr is not a viable replacement for Permalloy in cryogenic memory junctions, despite its promising low switching fields of a few millitesla.

Load-bearing premise

The numbers 2.3 nm and 0.36 nm come from fitting the data to one assumed functional form, Eq. (4), and the paper itself notes that NiFeCr junctions may not lie cleanly in either the diffusive or intermediate transport regime; if another valid function fits the data, those values change.

Editorial extensions

If this is right

NiFeCr should not be adopted as the soft magnetic layer in cryogenic memory circuits that need π-junctions with large critical current density.
The short 0.36 nm decay length means NiFeCr junctions must be kept extremely thin, tightening fabrication tolerances compared with NiFe.
Because the π-state thickness rose from 1.49 nm to 2.30 nm while magnetization fell, the magnetic switching energy, which scales as $M_s^2 t_F^2$, is barely reduced by Cr doping.
The close similarity between NiFeCr and NiFeMo behavior near the 0–π transition suggests that alloying-induced softening generally comes with a suppressed supercurrent.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the same trade-off holds for other doped Permalloys, the search for a cryogenic-memory soft magnet should prioritize alloys whose exchange stiffness and mean free path survive doping, not merely those with lower saturation magnetization.
The sub-nanometer decay length could be dominated by spin-flip scattering from Cr impurities; a testable extension would be to measure NiFeCr junctions with different Cr concentrations and see whether $\xi_{F1}$ tracks the Cr content.
The single-lobe data leave the fitted functional form unverified beyond 3.7 nm; mapping a second 0–π oscillation would either confirm the assumed fit or reveal that the 2.3 nm and 0.36 nm values are artifacts of the chosen functional form.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a useful, honest experimental paper from the Birge group, and it delivers a clear negative result for NiFeCr as a cryogenic-memory material. The 0–π transition at 2.3 nm, the rapid 0.36 nm decay length, and the roughly two-order suppression of Ic in the π-state are the first transport measurements on NiFeCr Josephson junctions, extending the group's systematic alloy comparison (NiFe, NiFeMo, NiFeCu, NiFeNb). The magnetic characterization is also careful: Ms = 579 ± 16 kA/m for NiFeCr versus 935 ± 17 for NiFe, with dead-layer estimates, and coercivity versus thickness data. That's real added value for material-selection tables.

The central qualitative claim is robust. The IcRN(dF) data show a clear minimum near 2.3 nm for NiFeCr and a much faster decay than NiFe; this does not depend on the specific fit form. The conclusion that NiFeCr is not a good replacement for Permalloy in π-junction memory follows directly.

Where I part ways with the abstract's precision: the quantitative numbers d0π = 2.30 ± 0.01 nm and ξF1 = 0.36 ± 0.01 nm come from fitting Eq. (4), a damped sinusoid whose regime of validity for NiFeCr the authors explicitly say is unclear. The reported uncertainties are pure fit statistics; they don't include model choice or the 0.5 nm thickness step calibration. The switching-energy conclusion (Esw ∝ Ms^2 tF^2) is an estimate, not a measurement, and depends on d0π. So the abstract overstates certainty, but the paper itself is more careful and acknowledges the regime caveat. The treatment of the couple of second-run points near the transition is vague—the authors mention exceptions to the fit but don't describe how they were handled in the fitting. That's a legitimate referee request.

The stress-test note makes a fair point but doesn't overturn the paper. A different functional form might shift d0π by a few tenths of a nanometer, which could change the 'switching energy hardly changed' conclusion quantitatively, but not the qualitative rejection of NiFeCr for memory applications.

Who's this for? Researchers working on ferromagnetic Josephson junctions, particularly those doing material screening for superconducting memory. The paper is well-written, self-critical, and the data appear to be taken carefully. I'd send it to peer review; a competent referee should ask for model-uncertainty quantification and clarification of the fitting exclusion, but this is not a desk-reject.

Referee Report

4 major / 4 minor

Summary. The paper reports a comparative study of ferromagnetic Josephson junctions with NiFeCr (Ni73Fe18Cr9) and NiFe (Ni82Fe18) barrier layers, motivated by the search for a soft-magnetic material with low switching field and energy for cryogenic memory applications. The authors characterize the magnetization, coercivity, and Josephson critical current of both systems, and fit the measured IcRN versus ferromagnetic-layer thickness to an exponentially decaying sinusoidal function (Eq. 4). From these fits they extract a 0–π transition thickness d0π = 2.30 nm for NiFeCr versus 1.49 nm for NiFe, and a decay length ξF1 = 0.36 nm versus 0.67 nm. The central qualitative conclusion is that Cr doping reduces the magnetization by roughly one-third but suppresses the critical current by nearly two orders of magnitude in the π state, making NiFeCr unattractive for memory applications requiring large critical currents. The manuscript also reports switching-field measurements showing a few-mT coercivity for the thinnest NiFeCr films.

Significance. If the quantitative claims held, this would be a useful negative result for the superconducting-memory community: it identifies a specific alloy that initially appears promising—because Cr doping reduces Ms without destroying soft magnetic behavior—but that fails in the Josephson-junction context because of the short decay length and low critical current. The qualitative finding is directly visible in the raw IcRN data: NiFeCr junctions carry substantially smaller supercurrents than NiFe junctions across the measured thickness range, and the suppression is not a fitting artifact. The paper also provides useful complementary data on magnetization, dead-layer thickness, and coercivity. The main value is therefore the experimental comparison, not the extracted parameters. The extracted d0π and ξF1 values and the switching-energy comparison are model-dependent, because Eq. (4) is an assumed fitting form whose physical regime for NiFeCr is explicitly uncertain. The manuscript would be strengthened by clearly separating the robust qualitative conclusions from the model-dependent quantitative parameters.

major comments (4)

[§IV, Eq. (4)] The quantitative parameters in Table I and in the abstract—d0π = 2.30 nm and ξF1 = 0.36 nm for NiFeCr—are obtained by fitting the data to the exponentially damped sinusoid of Eq. (4). The paper states in §IV that it is not clear whether the NiFeCr junctions fall into the diffusive or intermediate limit, and that Eq. (4) is introduced only as an approximate model for both, rather than being derived from either limit. The functional form directly determines the extracted d0π and ξF1 values, so the reported precision of ±0.01 nm overstates what the data establish. Please quantify the model dependence by, for example, fitting the data with alternative physically motivated forms (e.g., independent decay and oscillation lengths without the absolute-value sine, or a full diffusive-limit Usadel expression) and reporting how d0π and ξF1 shift, or by presenting these parameters with a model-dependent systematic uncertainty.
[§IV, Fig. 4(a)] The text reports that the fit is good 'with the exception of a couple of NiFeCr junctions fabricated in a second sputtering run with thicknesses very close to the 0−π transition', but the paper does not describe how those points were treated in the fit, how many points were excluded, or what criterion was used for exclusion. Since those points lie precisely in the thickness range that determines the reported d0π = 2.30 ± 0.01 nm, the selection rule matters. Please state the exclusion criterion, show the fit with and without those points, or justify their removal with a quantitative outlier test.
[Table I] The quoted uncertainties (0.01–0.03 nm) are only the statistical errors from the nonlinear least-squares fits. They do not include systematic contributions from the 0.5 nm nominal thickness steps, the ±0.05 nm dead-layer correction determined from the magnetization intercept, or run-to-run variations between sputtering runs. The abstract's two-significant-digit values are therefore presented with false precision. Please report systematic uncertainties arising from thickness calibration, dead-layer uncertainty, and run-to-run reproducibility, and propagate them into the switching-energy estimate in the conclusion.
[§V, Conclusion] The claim that 'the NiFeCr thickness required to achieve the π state increased almost inversely proportionately to the decrease in magnetization, so that the switching energy is hardly changed' relies on the model-dependent d0π value and on the substitution Esw ∝ Ms^2 tF^2. The ratio Ms(NiFe)/Ms(NiFeCr) ≈ 1.61 and the ratio d0π(NiFeCr)/d0π(NiFe) ≈ 1.54 give a switching-energy ratio near unity only for the specific fitted d0π values. A 0.2 nm shift in d0π(NiFeCr)—well within the plausible systematic uncertainty given the thin-film thickness control—changes the switching-energy ratio by roughly 20%. The conclusion should either carry an explicit caveat that this estimate is contingent on the Eq. (4) fit, or be rephrased to distinguish the measured quantities from the derived estimate.

minor comments (4)

[§III A, Fig. 2 caption] The caption's 'msat/Area' should be typeset consistently (e.g., as msat/Area with subscripts), and the text contains a typo: 'remanance' should be 'remanence'.
[§III B, Eq. (1)] The RSJ expression V = sign(I)RN ℜ{sqrt(I^2 − Ic^2)} would be clearer if the sign convention for Ic (positive critical current) and the branch of the square root were stated explicitly.
[Fig. 4 caption] The caption uses 'dNiFe' in panel (b) but the text refers to 'dNiFe'; please use a single notation for the ferromagnetic-layer thickness, e.g., dF, in both panels and in Table I.
[§IV, second paragraph] The sentence 'the figure in panel (b) was published previously in Ref. 40' should clarify whether the NiFe data are reproduced from that reference or remeasured for this work, since Fig. 4(b) appears to include a previously published data set.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's claims are direct measurements and fits, with fit parameters reported as such rather than as predictions.

full rationale

This is an experimental comparison paper. The central claims—NiFeCr carries much less supercurrent than NiFe, has a 0–pi transition near 2.3 nm, and has a short decay length—are supported by direct I–V and magnetization measurements. Equation (4), IcRN = V0 exp(-dF/xi_F1)|sin((dF - d0pi)/xi_F2)|, is explicitly introduced as an approximate model for both diffusive and intermediate limits, and the paper states it is not clear which regime applies to NiFeCr. That is a stated assumption and a limitation, not a circular step: d0pi and xi_F1 are fit parameters of the model, tabulated as such in Table I, and the qualitative deep minimum in IcRN is observed directly. The comparison NiFe data come from the group's prior published measurements (Ref. 40), which are independent data rather than a self-citation chain or a uniqueness theorem. No load-bearing claim is justified by citing the authors' own unverified result. The quantitative values in the abstract inherit the uncertainty of Eq. (4), but that is a model-robustness concern, not circularity per the definitions used here.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The paper's quantitative conclusions rest on a small number of fitted parameters and modeling assumptions. The main free parameters are the coefficients of the phenomenological IcRN(dF) fit (Eq. 4), which produce the headline values of 2.30 nm transition thickness and 0.36 nm decay length, plus the measured saturation magnetizations used in the switching-energy estimate. The key axioms are the assumed validity of the damped-sinusoid approximation, the Stoner-Wohlfarth scaling argument, and the standard Josephson-junction models used to extract Ic and IcRN from raw data. No new physical entities are introduced.

free parameters (9)

V0 (NiFeCr) = 527 ± 42 µV
Overall magnitude scale in Eq. (4), fit to IcRN vs dNiFeCr; not physically interpreted.
ξF1 (NiFeCr) = 0.36 ± 0.01 nm
Exponential decay length of IcRN in Eq. (4); central quantity in the abstract claim that supercurrent decays over 0.36 nm.
ξF2 (NiFeCr) = 0.67 ± 0.03 nm
Oscillation period length in Eq. (4); underconstrained without the second 0-π transition, as the authors state.
d0π (NiFeCr) = 2.30 ± 0.01 nm
First 0-π transition thickness from Eq. (4); central to the claim that NiFeCr π-state requires 2.3 nm.
V0 (NiFe) = 329 ± 48 µV
Same fit parameter for NiFe reference junctions.
ξF1 (NiFe) = 0.67 ± 0.03 nm
Decay length for NiFe reference.
d0π (NiFe) = 1.49 ± 0.01 nm
0-π transition thickness for NiFe reference.
Ms (NiFeCr) = 579 ± 16 kA/m
Saturation magnetization from linear fit of moment per area vs thickness; used to estimate switching energy and compare with Permalloy.
Ms (NiFe) = 935 ± 17 kA/m
Saturation magnetization of NiFe from the same fit; comparison benchmark for the switching-energy argument.

assumptions (5)

ad hoc to paper The 0-π transition and oscillatory decay of IcRN with F-layer thickness can be modeled by the exponentially damped sinusoid Eq. (4) in both the diffusive and intermediate limits.
The paper states in Section IV that it is not clear whether NiFeCr junctions fall into either theoretical regime, and Eq. (4) is introduced as an approximation to both. All quantitative parameters (ξF1, ξF2, d0π) are extracted from this assumed form.
domain assumption Stoner-Wohlfarth scaling for a soft magnetic memory element: Hsw ∝ MstF and Esw ∝ Ms^2 tF^2.
Used in the Introduction and Conclusion to infer that switching energy is hardly changed when Ms drops and tF rises. Applies to coherent rotation, not domain-wall motion; the paper invokes it for small elliptical nanomagnets.
domain assumption The magnetization inside the Josephson junction is uniform and contributes to the flux as Φ = ... + μ0 M w dF (Eq. (3)).
Used to fit Ic(H) Airy patterns and extract Ic0. Ignores nonuniform magnetization, vortices, and fringe fields; the text calls it an approximation.
domain assumption The I-V characteristics follow the Resistively Shunted Junction model, or the Ivanchenko-Zilberman model with an effective noise temperature near 13 K for low-Ic samples.
Standard models used to extract Ic and RN from raw traces; the paper notes substantial rounding for the lowest-current samples.
domain assumption The measured composition and magnetic properties of the films, including the antiparallel Cr moment cited from Devonport et al., apply to the ferromagnetic layers inside the Josephson junctions.
The interpretation of the reduced Ms and shifted 0-π transition in terms of exchange energy relies on this transfer of thin-film material parameters to the junction geometry.

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Pith. "Pith review of Comparison of NiFeCr and NiFe in ferromagnetic Josephson junctions." pith.science (2026). https://pith.science/paper/LDFD5757

@misc{pith2026250106845,
  author       = {Pith},
  title        = {Pith review of: Comparison of NiFeCr and NiFe in ferromagnetic Josephson junctions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LDFD5757}},
  note         = {Machine review of arXiv:2501.06845}
}

abstract

Josephson junctions containing ferromagnetic materials are under consideration for applications in digital superconducting logic and memory. Some memory applications rely on the ability to reverse the magnetization direction of a "soft" magnetic layer within the junction using a small local magnetic field generated on the chip. It is crucial, therefore, to find a suitable soft magnetic material with a low switching field and low switching energy. A popular magnetic material for such applications is Ni$_{80}$Fe$_{20}$, also known as Permalloy, however Permalloy has a rather large magnetization, leading to large magnetic switching energies. In this work we explore Cr-doped Permalloy, specifically Ni$_{73}$Fe$_{18}$Cr$_{9}$, which has a saturation magnetization just under two-thirds that of Permalloy. Josephson junctions containing this NiFeCr alloy undergo a 0-$\pi$ transition at a NiFeCr thickness of 2.3 nm, and the critical supercurrent decays in the alloy over a short characteristic length of 0.36 nm. Switching fields of a few millitesla are promising, but the short decay length and overall small values of the critical current in the Josephson junctions may preclude the use of NiFeCr in current cryogenic memory technologies.

Figures

Figures reproduced from arXiv: 2501.06845 by the authors.

**Figure 1.** FIG. 1. Magnetization ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 3.** FIG. 3. Critical current ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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